Following 24 hours of victory celebrations in Baghdad, there are fears today that the war, far from ending, could simply be moving into a far more intractable low-intensity phase in which bunker-busting bombs and other hi-tech weapons are of little use.

Yesterday, a particularly bad sign was the killing, in Iraq's holiest Shia mosque, of Abdul Majid al-Khoei, a US-backed cleric who had been living in exile in London until last week. It is unclear whether his death was the work of Saddam Hussein loyalists or a rival Shia group but, either way, the implications are alarming.

Mr al-Khoei was the son of Ayatollah Sayed al-Qasim al-Khoei, the leader of much of the Shia world until 1992 when he died, under house arrest, in Najaf.

The importance of his murder may be difficult to appreciate in countries in which religious leaders carry little political weight, but the closest British parallel is probably with Thomas Becket, the Archishop of Canterbury who, 833 years ago, was assassinated for supporting the authority of the Pope over King Henry II.

There was also another suicide bombing last night, when a man wearing an explosives-packed vest attacked a US checkpoint in Saddam City, the Shia suburb of Baghdad. Conflicting reports of casualties ranged from four US marines wounded to several dead.

Overnight, Iraqi gunmen, apparently from Shia slums in eastern Baghdad, fought a fierce hour-long battle with Fedayeen paramilitaries loyal to Saddam, according to US military sources and a Reuters news agency report.

So far, there has been no serious effort to stop the looting in Baghdad. US officials expect it to fizzle out naturally when there is nothing left to loot, although reports that Iraqis have even been stripping electrical wiring from buildings suggest that it may continue for some time.

If the experience in Basra is anything to judge by, this spontaneous crimewave could be followed by a more organised phase as armed gangs move in. Before the war, US and British planners had hoped that enough of Iraq's administration and security forces would be left intact to keep the country running but, in key places, they have either been destroyed or gone underground.

This should be less of a problem in the north, where the Kurds have been governing themselves for years, and are well organised. Elsewhere, the situation in smaller Iraqi towns which have not been touched by the war is largely unknown, and may be salvageable.

However, in areas such as Baghdad, in which all government has evaporated, there are now three basic choices:

1. Restoration of Ba'athists from the middle and lower ranks, assuming that they can be found and are willing to serve. This carries the risk of reinstating old patterns of misrule and corruption.

2. The development of local fiefdoms based around tribal or religious figures who are capable of maintaining order, but may turn out to be no less tyrannical than the previous regime.

3. Rebuilding the system from scratch, which would take months of recruitment and training.

All these factors point to the need for a prolonged US and British presence, which opponents will characterise as "occupation", as the Syrian government did yesterday.

Attacks by mujahideen, and possibly underground Ba'athists, will seek to push the US and British towards repressive measures in order to justify the term "occupation" and encourage others to join the struggle against it.

The model here is the Soviet invasion of Afghanistan in the 80s, and the resistance to it. This, in the eyes of Islamists, not only led to the creation of al-Qaida, but also brought about the collapse of a superpower. The strategy is clear, although it's much too early to judge whether it has any chance of succeeding in Iraq.

George Bush and Tony Blair both gave speeches (dubbed into Arabic) on the new Towards Freedom TV station yesterday although, with no electricity in most of Baghdad, it is doubtful whether many people could have watched it.

Mr Blair promised to see the war through to the end. Mr Bush said that the US would respect Iraq's "great religious traditions, whose principles of equality and compassion are essential to Iraq's future".

In northern Iraq early today, US and Kurdish forces reportedly captured Mosul, Iraq's third city, without a fight. Kurdish paramilitaries have promised to hand over the important oil city of Kirkuk to US troops later today.

Kirkuk, the traditional capital of the Kurds, was taken by a mixture of Kurdish guerrillas and US special forces yesterday, but neighbouring Turkey, fearful of increased Kurdish power, has been insisting that the Kurds must not be allowed to keep it.

There is growing debate on the internet about the toppling of Saddam Hussein's statue in Baghdad, and the extent to which it was stage-managed for the TV cameras.

Numerous Guardian readers have pointed out an aerial photograph of the scene, showing how small the crowd was. However, it is not known at what point the photograph was taken.

The picture is broadly consistent with remarks about the size of the crowd made by a BBC reporter who was on the spot at the time.

There are claims that the US flag draped over the statue's head was one that had been flying over the Pentagon at the time of the September 11 terrorist attacks, although this may just be a rumour.

The Iraqi flag produced after the stars and stripes appears to have been carefully selected. It was not the current flag, but the pre-1991 design. Shortly before the 1991 Gulf war, Saddam Hussein had the words Allahu Akbar (God is greatest) inserted between the stars, and these were missing from the flag used on Wednesday.

Discussion of this "defining moment" looks set to continue, and any further information will be welcome.